General Relativity & The Sun: Does it Revolve Around Earth?

[JohnNemo]

The discussion here

https://www.physicsforums.com/threads/general-relativity-the-sun-revolves-around-the-earth.245334/

concludes that in general relativity there are no privileged reference frames so that, for example, it would be valid to use the Earth as a reference frame and say that distant stars are orbiting the Earth approximately once every 24 hours.

However if distant stars are orbiting the Earth once every 24 hours, would those distant stars not be traveling faster that the speed of light (which is not supposed to be possible)?

 

[Orodruin]

No. It would only be true about the coordinate velocities. What you need to compare with is how light would move at the same place as the distant stars.

 

[PeroK]

The discussion here

https://www.physicsforums.com/threads/general-relativity-the-sun-revolves-around-the-earth.245334/

concludes that in general relativity there are no privileged reference frames so that, for example, it would be valid to use the Earth as a reference frame and say that distant stars are orbiting the Earth approximately once every 24 hours.

However if distant stars are orbiting the Earth once every 24 hours, would those distant stars not be traveling faster that the speed of light (which is not supposed to be possible)?

In the past - perhaps even these days - sailors would navigate at sea using the position of the stars. They were using the reference frame of the Earth.

In a sense, therefore, this frame has always been valid. The question, however, is how you describe the laws of physics in such a frame. Newton's laws don't hold - the stars accelerate without any force on them. The laws of SR don't hold - the stars have coordinate velocities beyond the speed of light.

It's inevitable, therefore, that if you allow these frames in GR, then the form that the laws of physics take cannot be as simple as they are in SR.

In GR light follows what are called null geodesics and, as you would guess, this implies that light travels (locally) in every inertial reference frame at the invariant speed $c$ and all massive particles travel locally at less than $c$.

 

[Ibix]

travelling faster that the speed of light (which is not supposed to be possible)?

It's not possible in an inertial reference frame. An inertial reference frame is one where things that feel no forces move in straight lines. But in your rotating reference frame an object that feels no forces will orbit the Earth - moving in a circle. So this is not an inertial reference frame so the speed limit doesn't apply.

This is just an effect of using a complicated reference frame. You will always find that light wins a race with anything else even in this rotating frame. It's just that there isn't a simple relationship between the actual physics and the description of the physics that you picked.

 

[sweet springs]

Hello.
In the distant region of the revolving Earth system where $$\rho$$, the radius from the Earth axis, is
$$\rho>\rho_0=\frac{c}{\omega}=\frac{299792458}{\frac{2\pi}{24*60*60}}[m]=4.122*10^{12}[m]$$,
no physical particles or bodies can stay still in the revolving Earth system.

The invariance of maximum propagation speed, or light speed, applies in local time and coordinate of a frame of reference physical reality of which is proved if there can exist particles or bodies at rest locally in that frame of reference.

So you do not worry about a contradiction you mentioned.

 

[JohnNemo]

No. It would only be true about the coordinate velocities. What you need to compare with is how light would move at the same place as the distant stars.

OK. I think I understand that: co-ordinate velocity can exceed c.

So, with that objection disposed of, is it really true that there is no way of telling whether the Earth is spinning, or whether the Earth is fixed and the stars are orbiting it every 24 hours? You can choose whatever reference frame you want and all the laws of physics work OK from whichever reference frame you use?

 

[Orodruin]

So, with that objection disposed of, is it really true that there is no way of telling whether the Earth is spinning, or whether the Earth is fixed and the stars are orbiting it every 24 hours? You can choose whatever reference frame you want and all the laws of physics work OK from whichever reference frame you use?

No. As explained in #4.

 

[JohnNemo]

No. As explained in #4.

OK. How can you tell if you are "really" rotating in absolute terms? What kind of experimental result would establish this?

 

[phinds]

OK. How can you tell if you are "really" rotating in absolute terms? What kind of experimental result would establish this?

Well, for the Earth, for example, the Foucault pendulum does a good job.

 

[Ibix]

You can choose whatever reference frame you want and all the laws of physics work OK from whichever reference frame you use?

You can work in any reference frame you choose. The maths will be hideously complicated if you don't pick a sensible one for the problem at hand.

OK. How can you tell if you are "really" rotating in absolute terms? What kind of experimental result would establish this?

It depends on your philosophical inclination, basically. You can certainly detect whether or not you are using an inertial reference frame - just let go of something. If it starts to move relative to whatever you regard as stationary and there are no forces (wind, magnetism, whatever) then you're using a non-inertial frame. If it stays stationary then you're in an inertial frame (or your experiment isn't precise enough). For example, lay a pen on your dashboard then drive round a corner or stamp on the accelerator. The pen will start to move relative to the car, from which you can deduce that the car is not an inertial reference. See also hurricanes.

But none of that tells you whether the car is turning or the universe is turning around the car. It seems unlikely that the universe really revolves around me, but I can certainly describe it as doing so. If I just want to think about whether my coffee is going to spill when I take the next corner, "the world is turning around me" might be the smarter viewpoint. If I want to model a black hole a few thousand light years away I'd be daft to pick a me-centered reference frame.

Basically, I don't think there's a clear physical definition of "really" rotating. We can talk about reference frames, and there are certainly different types. But they're pinned to some relevant bit of physics, not necessarily any fundamental reality. Whatever that might mean.

 

[Nugatory]

OK. How can you tell if you are "really" rotating in absolute terms? What kind of experimental result would establish this?

An accelerometer will detect your centripetal acceleration. This works even if you and your lab equipment are sealed up in a windowless room with no input from the outside world.

It gets trickier if you are in a curved spacetime so that there are significant gravitational effects. For example there is no way of detecting that your sealed and windowless room is in orbit around the Earth and changing speed and direction under the influence of the Earth's gravity, instead of moving in a straight line at a constant speed in empty space - it's just freefall either way. What's going on here is that in a curved spacetime there's no single quantity that you can call the "speed" of a distant object relative to you because there is no inertial frame that includes both you and the distant object. The distant object will never move faster than a flash of light that is near it, but depending on my choice of coordinates neither the speed relative to me of that distant object nor of the flash of light will have anything to do with $c$, the speed of light in a vacuum in my lab.

 

[JohnNemo]

Well, for the Earth, for example, the Foucault pendulum does a good job.

The Foucault pendulum goes through 360 degrees every 24 hours. As I understand it you are saying that it would only do this if the Earth were rotating in absolute terms (so the fact that it does this proves that it is the Earth which is rotating).

So, in your understanding, if the Earth were stationary and the distant starts were orbiting it every 24 hours, how would you expect the Foucault pendulum to behave then? What difference would you expect to see?

 

[PeterDonis]

The Foucault pendulum goes through 360 degrees every 24 hours. As I understand it you are saying that it would only do this if the Earth were rotating in absolute terms (so the fact that it does this proves that it is the Earth which is rotating).

It proves that the Earth is rotating relative to the distant stars.

if the Earth were stationary and the distant starts were orbiting it every 24 hours, how would you expect the Foucault pendulum to behave then?

The same, because the relative rotation is the same.

 

[PeterDonis]

for the Earth, for example, the Foucault pendulum does a good job.

It does a good job of showing that the Earth rotates relative to the distant stars. But that's still relative rotation, not "absolute rotation".

The best candidate for an indicator of "absolute rotation" is, as @Nugatory said, proper acceleration as measured by an accelerometer. Or, equivalently, you can run an experiment like Newton's bucket--Newton talked about a bucket full of water, and using it to distinguish "absolute rotation" by the shape of the water's surface (flat if not rotating, concave if rotating). But in GR, even this can be considered relative, since which states of the bucket are which is determined by the geometry of spacetime, which is determined by the distribution of stress-energy. So you can consider the bucket's rotation, or lack thereof, as being "relative" to the distribution of stress-energy.

 

[Orodruin]

In this context I cannot help but quoting one of the limericks from https://www.physics.harvard.edu/academics/undergrad/limericks

On a merry-go-round in the night,
Coriolis was shaken with fright.
Despite how he walked,
'Twas like he was stalked,
By some fiend always pushing him right.

 

[JohnNemo]

But in GR, even this can be considered relative, since which states of the bucket are which is determined by the geometry of spacetime, which is determined by the distribution of stress-energy. So you can consider the bucket's rotation, or lack thereof, as being "relative" to the distribution of stress-energy.

So does this mean that it is impossible to tell whether the bucket is rotating (in absolute terms)? The behaviour of the water could be due to a rotating bucket. But equally if the bucket were stationary and the starts were orbiting it quickly, the gravitational field thus created would account for the bahaviour of the water.

 

[PeroK]

OK. How can you tell if you are "really" rotating in absolute terms? What kind of experimental result would establish this?

Given that this is a B level thread, I think that experiments such as Foucault's pendulum is a satisfactory answer.

At an intermediate level you may study rotating reference frames in more detail and derive the Coriolis force or the equation for the precession of Foucault's pendulum.

There is a risk that the more advanced ideas being expounded here cloud what is otherwise a plain matter and confuse you to the point where you cannot learn the basics of physics without digesting more advanced concepts.

That said, you did ask the question. And you did ask about reference frames in GR.

 

[DrGreg]

You could also use a gyroscope.

 

[JohnNemo]

Given that this is a B level thread, I think that experiments such as Foucault's pendulum is a satisfactory answer.

At an intermediate level you may study rotating reference frames in more detail and derive the Coriolis force or the equation for the precession of Foucault's pendulum.

There is a risk that the more advanced ideas being expounded here cloud what is otherwise a plain matter and confuse you to the point where you cannot learn the basics of physics without digesting more advanced concepts.

That said, you did ask the question. And you did ask about reference frames in GR.

Sorry. My mistake. Would it be in order to re-post my question a an I level thread?

 

[PeterDonis]

does this mean that it is impossible to tell whether the bucket is rotating (in absolute terms)?

With the meaning you appear to be giving the term "absolute rotation", yes, because there is no such thing as "absolute rotation" with that meaning.

The behaviour of the water could be due to a rotating bucket. But equally if the bucket were stationary and the starts were orbiting it quickly, the gravitational field thus created would account for the bahaviour of the water.

A better way of saying this is that it is the relative rotation of the water and the stars that makes the bucket concave. You can describe this relative rotation in a frame where the bucket is stationary, or a frame where the stars are stationary. Both are valid coordinate charts and can describe the same physical situation.

 

[PeterDonis]

Would it be in order to re-post my question a an I level thread?

If you are ok with the discussion being at the "I" level, I can just change the level of this thread to correspond.

 

[JohnNemo]

If you are ok with the discussion being at the "I" level, I can just change the level of this thread to correspond.

Yes. Please.

 

[PeroK]

Sorry. My mistake. Would it be in order to re-post my question a an I level thread?

It's more for you to decide what level of physics you want to understand. I checked your profile and is says "completed undergrad". Was that in physics?

 

[JohnNemo]

If you are ok with the discussion being at the "I" level, I can just change the level of this thread to correspond.

OK so apologies for things going off at a tangent.

Can I restart by asking this question:

Is it really true that there is no way of telling whether the Earth is spinning, or whether the Earth is fixed and the stars are orbiting it every 24 hours? You can choose whatever reference frame you want and all the laws of physics work OK from whichever reference frame you use?

 

[PeterDonis]

Is it really true that there is no way of telling whether the Earth is spinning, or whether the Earth is fixed and the stars are orbiting it every 24 hours?

The problem here is not the answer, it's the way you're asking the question. You are assuming that "the Earth is spinning" and "the Earth is fixed and the stars are orbiting it every 24 hours" are two different possible ways the world could be. That's not the case. Both of these verbal descriptions correspond to the same physical situation--the same single way the world is.

You can choose whatever reference frame you want and all the laws of physics work OK from whichever reference frame you use?

Yes, because they are the same laws of physics regardless of which reference frame you use. You can't change the way the world is by changing reference frames. And changing reference frames is all that changes when you switch from "the Earth is spinning" to "the Earth is fixed and the stars are orbiting it every 24 hours". Nothing in the actual world changes; only your description of it does.

 

[JohnNemo]

Yes, because they are the same laws of physics regardless of which reference frame you use. You can't change the way the world is by changing reference frames. And changing reference frames is all that changes when you switch from "the Earth is spinning" to "the Earth is fixed and the stars are orbiting it every 24 hours". Nothing in the actual world changes; only your description of it does.

Has the equivalence you describe been generally accepted for, say, the lat 50 years? Has it ever been controversial or been seriously doubted?

 

[PeterDonis]

Has the equivalence you describe been generally accepted for, say, the lat 50 years? Has it ever been controversial or been seriously doubted?

As far as GR is concerned, just considering it as a physical theory, the equivalence has always been there and has never been seriously doubted.

However, it's worth noting that there is a long-standing debate over how "Machian" GR is, which often involves examples like the one we are discussing. Some people might misinterpret this as a debate about whether the equivalence really is generally accepted. It's not a debate about that. It's more of a philosophical debate about what different people think a theory "should" look like, and whether GR looks like that, and if not, what a more comprehensive theory that includes GR as a special case within its domain of applicability might look like.

 

[JohnNemo]

As far as GR is concerned, just considering it as a physical theory, the equivalence has always been there and has never been seriously doubted.

However, it's worth noting that there is a long-standing debate over how "Machian" GR is, which often involves examples like the one we are discussing. Some people might misinterpret this as a debate about whether the equivalence really is generally accepted. It's not a debate about that. It's more of a philosophical debate about what different people think a theory "should" look like, and whether GR looks like that, and if not, what a more comprehensive theory that includes GR as a special case within its domain of applicability might look like.

When people first come across relativity, there usually comes a point in the process of understanding where they say "yes, I can see that relative velocity (say) depends on the observer, but what is really happening, what is the real velocity?" And it takes a further leap to understand that not only is the answer unknown but that it is believed that the entity envisaged (absolute velocity) does not correspond to any physical reality.

I can conceive of two different types of possible more comprehensive theory

1. A theory shows that GR is wrong in certain circumstances within its own claimed domain of applicability. An example of this from the past would be Newton's theories - incorrect for high velocities (albeit still a very useful approximation for everyday practical purposes).

2. A theory which shows that there are objective reasons for preferring the view of one observer to another (not just for some immediate practical purpose but for objective reasons which might be expected to gain universal acceptance). An example of this might be the discovery of cosmic background radiation. I believe that some people at the time thought of this as bringing back the idea of absolute motion because it was possible to measure velocity relative to the background radiation and because the radiation was produced by the big bang (which was also presumed to be responsible for the laws of physics as we understand them) there was something special about it which might justify its use as the "standard" universal reference point for measuring absolute velocity. I think this suggestion did not gain much traction because cosmic radiation, like everything else, is affected by gravitation (and so is not fixed and uniform in the same way as the ether was envisaged as being) but this is just an example of a kind of theory which would not mean that GR was wrong but would mean that there were objective reasons for preferring one point of reference (or one class of points of reference) to another as some kind of standard.

Is the kind of comprehensive theory you mention 1, or 2, or something else?

 

[PeterDonis]

Is the kind of comprehensive theory you mention 1, or 2, or something else?

Not 1, because GR has very good experimental confirmation within its domain of applicability. So any more comprehensive theory would have to make the same predictions that GR does within that domain.

Not 2 as you state it, because the presence of something like the CMBR, which picks out a particular state of motion (the state in which the CMBR looks isotropic), does not mean there is "absolute motion" or an "absolute frame". It just means the stress-energy content of the universe has a particular configuration, and the laws of GR specifically relate the geometry of spacetime to the actual configuration of stress-energy, so different configurations of stress-energy lead to different spacetime geometries. That doesn't change any of the laws of physics, it just changes the particular solution of those laws that describes what you're interested in.

So the only option left is "something else", but it's not really possible to describe what that something else is, because if we knew that, we would already have the more comprehensive theory. The only thing we think we know about it is that it will be some kind of quantum theory of gravity (although even that is not universally believed; Freeman Dyson, for example, has speculated that maybe gravity simply isn't quantized, so the best we will be able to do is figure out how to have classical gravity--GR--coexist with quantum field theory for everything else).

 

[JohnNemo]

Yes, because they are the same laws of physics regardless of which reference frame you use. You can't change the way the world is by changing reference frames. And changing reference frames is all that changes when you switch from "the Earth is spinning" to "the Earth is fixed and the stars are orbiting it every 24 hours". Nothing in the actual world changes; only your description of it does.

From the Earth's reference frame, what accounts for the stars orbiting the Earth? I'm assuming that the Earth's gravity has a negligible effect on distant stars. Is it some kind of frame dragging effect which makes the stars circle the Earth?

 

[Orodruin]

From the Earth's reference frame, what accounts for the stars orbiting the Earth? I'm assuming that the Earth's gravity has a negligible effect on distant stars. Is it some kind of frame dragging effect which makes the stars circle the Earth?

The Coriolis force. Note that the Coriolis force actually gives you twice the force that would be required, but half of that is countered by the centrifugal force.

 

[JohnNemo]

The Coriolis force. Note that the Coriolis force actually gives you twice the force that would be required, but half of that is countered by the centrifugal force.

Sorry, my question was badly worded. By using the word "accounts" it sounded like I was asking a question about how Newtonian mechanics accounts for it by using fictitious forces.

What I meant to ask was: "In GR what is the cause (explanation) of the circular rotation of the stars"

 

[PeroK]

From the Earth's reference frame, what accounts for the stars orbiting the Earth? I'm assuming that the Earth's gravity has a negligible effect on distant stars. Is it some kind of frame dragging effect which makes the stars circle the Earth?

In one sense nothing needs to account for it. If you bounce up and down on a trampoline you could ask what accounts for everyone else bouncing down and up in your frame?

Whatever it is it's not the trampolinist's gravity!

Note that there are other rotating planets, with different angular velocity from the Earth. So, what forces are the distant stars supposed to feel?

And someone living on a distant planet will have no way to measure the effect of the Earth's rotation on them. Because there is none.

This is where is trying to grasp the I or A level answer you lose touch with the B level answer.

 

[PeroK]

Sorry, my question was badly worded. By using the word "accounts" it sounded like I was asking a question about how Newtonian mechanics accounts for it by using fictitious forces.

What I meant to ask was: "In GR what is the cause (explanation) of the circular rotation of the stars"

In GR the equations of motion come from the differential description of spacetime. In one reference frame the line element has a certain form, which leads to the geodesic equations, which leads to a solution for a particle or light ray in those coordinates.

If we change coordinates, we change the form of the line element, hence the geodesic equations hence get a different solution in those coordinates.

But, unless the maths has gone wrong, the two coordinate solutions must describe the same physical solution.

There is no cause in one frame or the other except that particles are following the natural paths through spacetime. Only the coordinate description of that spacetime and the associated geodesics changes.

 

[PeterDonis]

What I meant to ask was: "In GR what is the cause (explanation) of the circular rotation of the stars"

There is none. Causes don't change when you change frames, and something that doesn't even exist in one frame can't have a cause in another frame.

What you should be asking is, what is the cause of the relative rotation of the Earth and the distant stars. And the answer to that is the simple mundane answer: the geometry of spacetime and the worldlines of the matter inside the Earth and of the distant stars within that geometry. A further answer would go into the history of how those various pieces of matter came to have those worldlines, and how the spacetime of the universe and in the particular regions in question came to have its geometry.